On the other hand, the multi-field cosmology paradigm has proven to be an effective framework to account (in a single model) for several important characteristics/ingredients of the universe, e.g., early acceleration (inflation) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, dark matter [18]}, [19]}, [20]}, late acceleration [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}.
With respect to early and late acceleration, the crossing of the phantom divide line is a most wanted feature in scalar field cosmology; it has been shown that this crossing cannot be achieved by considering a single scalar field/fluid (unless stability is not demanded) [36]}. The standard quintom scenario [37]} considers two scalar fields, a quintessence and a phantom, in order to realize such crossing in a simple way. As a byproduct, quintom fields allow (in particular cases) the avoidance of the initial singularity by means of a bounce [38]} (see also the review [36]}). In the conventional quintom scenario (and in ordinary multi-field cosmology)
the scalar fields interact in the following way:
\(\mathcal {L}_\phi =\delta ^{ab}g^{\mu \nu }\nabla _\mu \phi _a\nabla _\nu \phi _b+V(\phi _a,\phi _b) \,.\) 
